A tearaway sheath assembly (100) having a splittable sheath tube (102) a splittable hub (110), a splittable valve (150) and a split cap (180). The valve (150) is of the elongated duckbill type and having a slit (158) almost completely across the distal end wall (154) such that two diverging sides (156) of the distal valve portion may be moved apart during insertion therethrough of a dilator or a catheter. A two-part cap (180) is affixed to the hub proximal end (120) and traps a seating flange (168) of the valve between itself and a seating groove (136) of the hub. Pairs of opposed gaps (184,122) of the cap (180) and the hub (110) are aligned with frangible sections or seams (108) of the sheath tube (102) and frangible sections (172) and slits (166) of the valve, facilitating splitting of the assembly (100) when desired by the practitioner to peel it away from the inserted catheter.